Mathematical Sciences: Topics in Statistical Theory

伯克教授将专注于在具有不平衡数据的双向表中测试交互作用，这个问题到目前为止还没有令人满意的无分布解决方案。辛格教授将继续研究重采样方法，引入按中心性顺序对定向数据进行排序的想法。这个排名提供了球面上的中位数的自然概念。他还将研究估计器和自适应估计效率的渐近下界。刘教授提出了与简单深度概念相关的问题。本课程将研究统计理论中的几个主题。潜在影响包括扩大统计方法对分类数据和稀疏数据结构的适用性。

Professor Berk will focus on testing for interaction in a two-way table with unbalanced data, a problem that has no satisfactory distribution-free solution to date. Professor Singh will continue work on resampling methods by introducing the idea of ranking directional data in the order of centrality. This ranking provides a natural concept of the median on a sphere. He will also work on asymptotic lower bounds of efficiency for estimators and adaptive estimation. Professor Liu pursues questions related to the notion of simplicial depth. Several topics in statistical theory will be investigated. The potential impact includes a broadening of the applicability of statistical methods for categorical data and for sparse data structures.